Trapping horizon

A trapping horizon is a hypersurface foliated by marginal two-surfaces with one null expansion zero and the other nonzero. A future outer trapping horizon has ${\theta }_{+}=0$, ${\theta }_{-}<0$ and ${\mathcal{L}}_n{\theta }_{+}<0$ for a future ingoing null normal $n$. Unlike an event horizon, this is a quasi-local definition. Under the null energy condition, a regular future outer horizon is spacelike or null. The ingoing derivative condition distinguishes its outer type from an inner trapping horizon.